If left wing insurgents started gaining momentum in their quest to take over germany during the german revolution, would the WAllies intervene in an attempt to stop a new soviet state from forming?
Yes. As Garrison said, they sent troops into Russia, so why wouldn't they do it here? Additionally, France has a vested interest in Germany (the Rhineland), and I doubt the communists would accept Versailles. Also Britain and America had a general anti-Communist sentiment and would rather see the Kaiser back than a second rate Lenin emerge. That said, they didn't intervene in Hungary, but IMO Germany would get the Russia treatment.
What would be the consequences of this?
Emergence of a Fascist style anti-Communist government à la Hungary/Italy. The Freikorps will be a major Political power in the immediate aftermath, so a Government run by them is very likely.
Not much, no one really wants him back by this point.
Would german soldiers be willing to serve with their former enemies in the fight against communism?
Yes, though it'll more a 'teeth gritted we're all in this together because if not then we're fucked' vibe than anything closely resembling friendly.
Is there a timeline concerning this?
I'll get back to you on this.